Characteristics of the patient group
Table 1 shows the summary of baseline characteristics and post-LT courses of the patient group. A total of 1512 LTs, 1153 LDLTs and 359 DDLTs were included to the study. Most of the recipients were male patients (78.0%, n=899 in LDLT and 67.1%, n=241 in DDLT) with mean age around 52. (52.8 ± 8.5 years in LDLT and 51.7 ± 10.4 years in DDLT) While mean donor age was 32.7 ± 11.6 years in LDLT, mean donor age of DDLT was 46.9 ±16.3 years in DDLT. While only 0.9% (n=10) of LDLTs were re-LT cases, 13.7% (n=49) of DDLT cases were re-LT cases. While 71.8% (n=827) of LDLT patients were hepatitis B-related, only 58.3% (n=208) of DDLTs were hepatitis B-related. While 10.0% (n=115) of LDLTs were alcohol-related, 26.1% (n=93) of DDLTs were alcohol-related. While more than half (n=670, 58.1%) of LDLT patients were HCC patients, only 38.4% (n=138) of DDLTs were HCC patients. Number of ABO incompatible LDLTs were 149 (n=12.9%). Mean MEAF score was 5.77 ± 1.66 in the LDLT cases compared to 7.12 ± 1.58 in DDLT cases. While 21.0% (n=242) of LDLT cases met the EAD criteria, 35.4% (n=127) of DDLT cases met the EAD criteria.
Prediction model using multivariable Cox regression
To build the best model for prediction, laboratory values were analyzed using univariable and multivariable models. Log2-transformation was performed to increase the predictability by changing the variable to a normal distribution.
Table 2 summarizes the results of the Cox regression models for LDLT. MEAF score as a continuous variable was significantly related to graft survival (HR=1.56, CI=1.35-1.80, P<0.001). EAD criteria as a binary variable was significantly related to graft survival (HR=3.28, CI=2.14-5.03, P<0.001). In the univariate analysis, log2-transformed ASTmax7 (HR=1.87, CI=1.60-2.18, P<0.001), log2-transformed TBmax3-7 (HR=1.62, CI=1.40-1.89, P<0.001) and log2-transformed INRmax3-7 (HR=3.99, CI=2.99-5.32, P<0.001) were related to graft survival. The ABC model for LDLT were constructed using three variables; log2-transformed ASTmax7 (HR=1.52, CI=1.29-1.80, P<0.001), log2-transformed TBmax3-7 (HR=1.44, CI=1.23-1.70, P<0.001) and log2-transformed INRmax3-7 (HR=3.29, CI=2.20-4.90, P<0.001).
C-index and time-dependent AUCs at 2 weeks and 4 weeks were compared between the ABC model and the other two models. The C-index of the ABC model for LDLT (0.73, CI=0.67-0.79) were higher compared to C-indexes of MEAF score (0.69, CI=0.63-0.76, P=0.03) and EAD criteria (0.64, CI=0.59-0.83, P=0.001). Time-dependent AUC at 2 weeks of the ABC model (AUC=0.96, CI=0.91-1.00) was significantly higher compared to that of EAD criteria (AUC=0.83, CI=0.75-0.92, P<0.001), while there was no significant difference compared to that of MEAF score. (AUC=0.90, CI=0.81-0.99, P=0.09, Figure 1A) Time-dependent AUC at 4 weeks of the ABC model (AUC=0.93, CU=0.86-0.99) was significantly higher compared to those of MEAF score (AUC=0.87, CI=0.78-0.95, P=0.02) and EAD criteria (AUC=0.84, CI=0.78-0.91, P=0.02, Figure 1B).
Table 3 summarizes the results of the Cox regression models for DDLT. MEAF score as a continuous variable was significantly related to graft survival (HR=1.65, CI=1.32-2.06, P<0.001). EAD criteria as a binary variable was significantly related to graft survival (HR=2.99, CI=1.66-5.37, P<0.001). In the univariate analysis, log2-transformed ASTmax7 (HR=1.57, CI=1.30-1.90, P<0.001), log2-transformed TBmax3-7 (HR=1.70, CI=1.37-2.10, P<0.001) and log2-transformed INRmax3-7 (HR=5.56, CI=3.46-8.94, P<0.001) were related to graft survival. The ABC model for DDLT were constructed using three variables; log2-transformed ASTmax7 (HR=1.19, CI=0.96-1.47, P<0.11), log2-transformed TBmax3-7 (HR=1.35, CI=1.05-1.73, P=0.02) and log2-transformed INRmax3-7 (HR=3.07, CI=1.67-5.64, P<0.001).
C-index and time-dependent AUCs at 2 weeks and 4 weeks were compared between the ABC model and the other two models. The C-index of the ABC model for DDLT (0.74, CI=0.65-0.83) was higher compared to C-index of EAD criteria (0.66, CI=0.59-0.73, P=0.002) whereas difference with MEAF score was statistically insignificant (0.71, CI=0.62-0.80, P=0.31). Time-dependent AUC at 2 weeks of the ABC model (AUC=0.98, CI=0.96-0.99) was significantly higher compared to that of EAD criteria (AUC=0.83, CI=0.81-0.86, P<0.001), while there was no significant difference compared to that of MEAF score. (AUC=0.88, CI=0.77-0.99, P=0.08, Figure 1C) Time-dependent AUC at 4 weeks of the ABC model (AUC=0.94, CU=0.89-1.00) was significantly higher compared to those of MEAF score (AUC=0.82, CI=0.68-0.96, P=0.02) and EAD criteria (AUC=0.81, CI=0.74-0.88, P<0.001, Figure 1D).
The predicted survival probabilities from Cox proportional hazards model for a set of covariates X may be estimated by the equation below where S0(t) is Breslow estimator for baseline survival function.
S(t, x) = S0(t)exp(xβ)
S0(t) = baseline survival function
xβ = {(log2ASTmax7 × 0.4205) + (log2TBmax3-7 × 0.3656) + (log2INRmax3-7 × 1.1893)} - 5.11 for LDLT
xβ = {(log2ASTmax7 × 0.1751) + (log2TBmax3-7 × 0.2986) + (log2INRmax3-7 × 1.1205)} -3.28 for DDLT
The baseline survival function is presented as tables in Supplementary table 1 and 2. The predicted probability of the recipient in a certain time point or the survival plot using the ABC model can be performed by putting the laboratory values into the Excel document provided as Supplementary material.
Apparent validation and internal validation
For internal validation, 20-time repeated 5-fold cross validation was applied to evaluate their performance. Apparent validation of the ABC model for LDLT showed C-index of 0.73 (CI=0.69-0.79), AUC at 2 weeks of 0.96 (CI=0.91-1.00), and AUC at 4 weeks of 0.93 (CI=0.86-0.99). Internal validation using 20-time repeated 5-fold cross validation of the ABC model for LDLT showed C-index of 0.68 (CI=0.66-0.69), AUC at 2 weeks of 0.91 (CI=0.87-0.96), and AUC at 4 weeks of 0.92 (CI=0.91-0.94). Apparent validation of the ABC model for DDLT showed C-index of 0.74 (CI=0.65-0.83), AUC at 2 weeks of 0.98 (CI=0.96-1.00), and AUC at 4 weeks of 0.94 (CI=0.89-1.00). Internal validation using 20-time repeated 5-fold cross validation of the ABC model for DDLT showed C-index of 0.68 (CI=0.66-0.70), AUC at 2 weeks of 0.86 (CI=0.80-0.92), and AUC at 4 weeks of 0.91 (CI=0.87-0.94).
Calibration plot
Calibration plots of ABC models at 2 weeks and 4 weeks through 1000 bootstrap resamples were performed. Figure 2 shows the calibration plots of ABC models for both LDLT and DDLT. The predicted probability and actual survival probability showed relatively competent calibration for ABC models for LDLT and DDLT.
Decision curve analysis
To evaluate the clinical usefulness of ABC model, decision curves were computed to calculate the net benefit. Figure 3 shows the decision curves of ABC models for LDLT and DDLT. For both 2 weeks and 4 weeks, and for both LDLT and DDLT, the decision curve constantly calculated above the zero-benefit line, showing beneficial expectation of the models.
Time-dependent AUC curves of ABC model
Time-dependent AUC curves of ABC models were illustrated in Figure 4. When the reference line was set as AUC of 0.75, the time-dependent AUCs were calculated to be above the reference line until 1 year in LDLT, and around 250 days in DDLT.